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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

The greatest common factor of two positive integers is X...

by AAPL » Fri Mar 23, 2018 6:02 am

The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

$$A.\ \frac{XY}{Z}$$
$$B.\ XZ+YZ$$
$$C.\ \frac{X}{Z}+Y$$
$$D.\ X+\frac{Y}{Z}$$
$$E.\ X+\frac{Z}{Y}$$

The OA is A.

I solved this PS question in the following way,

Say another integer is W,

Formula, GCF (W&Z)*LCM(W&Z) = W*Z

X*Y = W*Z

So,
$$W=\frac{X*Y}{Z}$$

Is there another approach to solve this question? For example, testing the answer choices. Can any experts help, please? Thanks!

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Source: Beat The GMAT — Problem Solving | Fri Mar 23, 2018 6:02 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

The greatest common factor of two positive integers is X...

by Brent@GMATPrepNow » Fri Mar 23, 2018 6:26 am

AAPL wrote:The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

$$A.\ \frac{XY}{Z}$$
$$B.\ XZ+YZ$$
$$C.\ \frac{X}{Z}+Y$$
$$D.\ X+\frac{Y}{Z}$$
$$E.\ X+\frac{Z}{Y}$$

--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of A and B)(least common multiple of A and B) = AB
Example: A = 10 and B = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

One of the two integers is Z
Let the other integer be Q.
So, our goal is to determine the value of Q

GIVEN:
The greatest common factor (divisor) of Z and Q is X.
The least common multiple of Z and Q is Y.

Take the formula: (greatest common divisor of A and B)(least common multiple of A and B) = AB
And plug in the given info to get: (X)(Y) = ZQ
In other words: XY = ZQ

Divide both sides by Z to get: XY/Z = Q

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

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by [email protected] » Fri Mar 23, 2018 12:46 pm

Hi AAPL,

We're told that the greatest common factor of two positive integers is X, the least common multiple of these two integers is Y and one of the integers is Z. We're asked for the other integer. This question can be solved by TESTing VALUES.

IF... the two integers are 2 and 3, then...
the greatest common factor is 1, so X=1
the least common multiple is 6, so Y=6
In this situation, you can make Z either 2 or 3 (and the other number will be what you're looking for in the answers). There's only one answer that matches...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Mon Mar 26, 2018 4:46 pm

AAPL wrote:The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

$$A.\ \frac{XY}{Z}$$
$$B.\ XZ+YZ$$
$$C.\ \frac{X}{Z}+Y$$
$$D.\ X+\frac{Y}{Z}$$
$$E.\ X+\frac{Z}{Y}$$

We can follow the rule:

GCF of A and B x LCM of A and B = A x B

We can let the other number = n and create the equation:

XY = Zn

XY/Z = n

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]